Homogeneous properties of infinite dimensional spaces

  • 报告人: 高速教授教授
  • 报告人单位: 美国北德克萨斯大学
  • 报告地址: 数学学院西109
  • 报告时间: 2017年9月28日(周四)下午4:00--5:00
  • 主题摘要:
We consider several homogeneous properties of topological spaces including homogeneity, countable dense homogeneity, and strong local homogeneity. For any subset of the real line, we give complete characterizations on when the infinite power of the set is homogeneous and strongly locally homogeneous. For a Borel subset of the real line, we also obtain a complete characterization for when its infinite power is countable dense homogeneous. The problem for totally disconnected subsets of the real line is independent of the usual axioms of set theory. This is joint work with Cris Allen.